// ---------------------------------------------------------------------
// $Id$
//
-// Copyright (C) 1998 - 2013 by the deal.II authors
+// Copyright (C) 1998 - 2014 by the deal.II authors
//
// This file is part of the deal.II library.
//
* degree <i>n-1</i>. The quadrature weights are
* <i>2/(n(n-1)(P<sub>n-1</sub>(x<sub>i</sub>)<sup>2</sup>)</i>.
*
- * Note: This implementation has not yet been optimized concerning
- * numerical stability and efficiency. It can be easily adapted
- * to the general case of Gauss-Lobatto-Jacobi-Bouzitat quadrature
- * with arbitrary parameters <i>alpha</i>, <i>beta</i>, of which
- * the Gauss-Lobatto-Legendre quadrature (<i>alpha = beta = 0</i>)
- * is a special case.
+ * @note This implementation has not been optimized concerning
+ * numerical stability and efficiency. It can be easily adapted
+ * to the general case of Gauss-Lobatto-Jacobi-Bouzitat quadrature
+ * with arbitrary parameters $\alpha$, $\beta, of which
+ * the Gauss-Lobatto-Legendre quadrature ($\alpha = \beta = 0$)
+ * is a special case.
*
* @sa http://en.wikipedia.org/wiki/Handbook_of_Mathematical_Functions
* @sa Karniadakis, G.E. and Sherwin, S.J.:
*
* @author Guido Kanschat, 2005, 2006; F. Prill, 2006
*/
-template<int dim>
+template <int dim>
class QGaussLobatto : public Quadrature<dim>
{
public:
/**
- * Midpoint quadrature rule, exact for linear polynomials.
+ * A quadrature formula implementing the one-point, midpoint quadrature
+ * rule. This formula is exact for linear polynomials.
*/
template <int dim>
class QMidpoint : public Quadrature<dim>
/**
- * Simpson quadrature rule, exact for polynomials of degree 3.
+ * A quadrature formula implementing the Simpson quadrature rule (with 3
+ * quadrature points). This formula is exact for polynomials of degree 3.
*/
template <int dim>
class QSimpson : public Quadrature<dim>
/**
- * Trapezoidal quadrature rule, exact for linear polynomials.
+ * A quadrature formula implementing the trapezoidal quadrature rule. This
+ * formula is exact for linear polynomials.
+ *
+ * The class is poorly named since the proper name of the quadrature formula
+ * is "trapezoidal rule", or sometimes also called the "trapezoid rule". The
+ * misnomer results from the fact that its original authors's poor English
+ * language skills led them to translate the name incorrectly from the German
+ * "Trapezregel".
+ *
+ * @author Wolfgang Bangerth, 1998
*/
template <int dim>
class QTrapez : public Quadrature<dim>
};
/**
- * Milne-rule. Closed Newton-Cotes formula, exact for polynomials of degree 5.
- * See Stoer: Einführung in die Numerische Mathematik I, p. 102
+ * A quadrature formula implementing the Milne rule. The Milne rule is a
+ * closed Newton-Cotes formula and is exact for polynomials of degree 5.
+ *
+ * @sa Stoer: Einführung in die Numerische Mathematik I, p. 102
*/
template <int dim>
class QMilne : public Quadrature<dim>
/**
- * Weddle-rule. Closed Newton-Cotes formula, exact for polynomials of degree 7.
- * See Stoer: Einführung in die Numerische Mathematik I, p. 102
+ * A quadrature formula implementing the Weddle rule. The Weddle rule is a
+ * closed Newton-Cotes formula and is exact for polynomials of degree 7.
+ *
+ * @sa Stoer: Einführung in die Numerische Mathematik I, p. 102
*/
template <int dim>
class QWeddle : public Quadrature<dim>
/**
- * Gauss Quadrature Formula with logarithmic weighting function. This
- * formula is used to to integrate <tt>ln|x|*f(x)</tt> on the interval
- * <tt>[0,1]</tt>, where f is a smooth function without
+ * A quadrature formula implementing the Gauss quadrature formula with
+ * logarithmic weighting function. This
+ * formula is used to integrate $\ln|x|\;f(x)$ on the interval
+ * $[0,1]$, where $f$ is a smooth function without
* singularities. The collection of quadrature points and weights has
* been obtained using <tt>Numerical Recipes</tt>.
*
- * Notice that only the function <tt>f(x)</tt> should be provided,
- * i.e., $\int_0^1 f(x) ln|x| dx = \sum_{i=0}^N w_i f(q_i)$. Setting
+ * Notice that only the function $f(x)$ should be provided,
+ * i.e., $\int_0^1 f(x) \ln|x| dx = \sum_{i=0}^N w_i f(q_i)$. Setting
* the @p revert flag to true at construction time switches the weight
- * from <tt>ln|x|</tt> to <tt>ln|1-x|</tt>.
+ * from $\ln|x|$ to $\ln|1-x|$.
*
* The weights and functions have been tabulated up to order 12.
- *
*/
template <int dim>
class QGaussLog : public Quadrature<dim>
* for regular functions once you factored out the singularity.
*
* The weights and functions have been tabulated up to order 12.
- *
*/
-template<int dim>
+template <int dim>
class QGaussLogR : public Quadrature<dim>
{
public:
* used to integrate $g(x) = 1/R\ f(x)$, or simply $f(x)$, with the $1/R$
* factor already included in the quadrature weights.
*/
-template<int dim>
+template <int dim>
class QGaussOneOverR : public Quadrature<dim>
{
public:
const unsigned int vertex_index,
const bool factor_out_singular_weight=false);
private:
- /** Given a quadrature point and a degree n, this function returns
- * the size of the singular quadrature rule, considering whether
- * the point is inside the cell, on an edge of the cell, or on a
- * corner of the cell. */
+ /**
+ * Given a quadrature point and a degree n, this function returns
+ * the size of the singular quadrature rule, considering whether
+ * the point is inside the cell, on an edge of the cell, or on a
+ * corner of the cell.
+ */
static unsigned int quad_size(const Point<dim> singularity,
const unsigned int n);
};
class QSorted : public Quadrature<dim>
{
public:
- /** The constructor takes an arbitrary quadrature formula. */
+ /**
+ * The constructor takes an arbitrary quadrature formula.
+ */
QSorted (const Quadrature<dim>);
- /** A rule to reorder pairs of points and weights.*/
+ /**
+ * A rule to reorder pairs of points and weights.
+ */
bool operator()(const std::pair<double, Point<dim> > &a,
const std::pair<double, Point<dim> > &b);
};
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